Concept of “Alligation”-05

Question: Weights of two friends Ram and Shyam are in the ratio of 4: 5. Ram’s weight increases by 10% and the total weight of Ram and Shyam together becomes 82.8 kg., with an increase of 15%. By what percent did the weight of Shyam increase?  [Ans. (d) 19%]    

(a)  10%   (b) 15%   (c) 22%     (d) 19%    (e) None of these

Solution:

Detailed explanation: First Method: Given that the ratio of weights of Ram and Shyam is 4: 5. Ram’s weight increase by 10%, while overall weight (Total weight of Ram and Shyam) increases by 15%. The difference between 15 and 10 is 5 ≡ 5. The difference between Shyam’s weight (in %) and 15 (in %) is 4, which is equivalent to 4 (as 5 ≡ 5). So, the increase in weight of Shyam is ? – 15 = 4; or, ? = 15 + 4 = 19% Ans.  

Second Method: Since the ratio of weights of Ram and Shyam is 4: 5, so let the weights of Ram and Shyam are 400 and 500 years (Without altering the ratio, values may be changed); so that the total weight = 900 Kg.

Increase in Ram’s weight = 10% of 400 Kg = 40 Kg

Increase in total weight = 15% of 900 Kg = 135 Kg

Increase in Shyam’s weight = 135 Kg – 40 Kg = 95 Kg, which is out of 500 Kg.

Therefore, percentage increase in Shyam’s weight = 19% Ans. [95 out of 500 or, 190 out of 1000 or, 19 out of 100]